Patients will be stratified based on lifetime CD4 T-cell nadir (lowest measurement) into one of three groups. Group 1 will have a nadir of 200 CD4 cells/mm3; Group 2 will have a nadir greater than 200 CD4 cells/mm3; and patients with no documented nadir count available will join Group 3. Within each group, patients will be randomly assigned to one of two study arms. Arm A patients will receive pulses of potent ART with IL-2, while Arm B patients will receive pulses of potent ART alone. Patients in Arm A will receive potent ART with IL-2 given by subcutaneous injection twice daily for 5 days every 8 weeks for at least 17 weeks. Arm B patients will receive potent ART alone for at least 17 weeks. Both groups then go on treatment interruption for approximately 64 weeks, followed by potent ART alone for an additional 24 weeks. Patients will repeat this cycle of potent ART with or without IL-2, treatment interruption, and potent ART alone throughout the study. This study will last approximately 4 years.